Did you click 'Continue' after catching the Pokémon?
You have to do that for the capture to count.
The same goes for when you defeat a Pokémon in battle.
Only when you click 'continue' and reach the summary of results (including the EXP/Money you gained), does it get saved.

1st Edition is most important with event Pokémon.
Some event Pokémon are only distributed once. Therefore, all of these Pokémon will be 1st Edition.
However, some event Pokémon may be redistributed in the future. These Pokémon will be 2nd edition (or whatever else Patrick decided to call it).
Although these event Pokémon will still be valuable, to big collectors the 1st Edition Pokémon will likely be more valuable.

It's not specifically listed on Vortex where the magnetic fields are.
The magnetic fields correspond to the magnetic fields in the main games.
I will list these locations below.
In Sidequests, you go through all main game areas. This includes the areas with a magnetic field.
The 'numbers' you're referring to are the completed Sidequest battles. These are listed in Vortex as well.
After a certain amount of battles you'll enter Mt. Coronet in Sinnoh (I don't know exactly which battle is which area). This number is always the same. You'll be there for a few battles, and then exit and be in a new area.
While you are in Mt. Coronet in Sidequest, you can evolve Pokémon that need a magnetic evolution.
The same goes for all locations listed below. For example, if you replace Mt. Coronetin what I just wrote with Kalos Route 13, then you will have the special magnetic field as well.
All Magnetic Fields:
Hoenn - New Mauville
Sinnoh - Mt. Coronet
Unova - Chargestone Cave
Kalos - Route 13
Alola - Blush Mountain and Vast Poni Canyon.
The specific amount of battles you need to complete to get to each area I don't know.
All I have for you is the list of battles at which each Region starts and ends. Somewhere in there are the areas you're looking for. That way you'll at least have an approximation.
I hope this helped you enough.

I will be posting it somewhere, likely on wattpad, when it's out.
I've not written any chapters yet though, a lot is still in the planning phase.
The teams are almost fully worked out, and many characters and events throughout the fanfic have been decided on. I'm super excited to write and release the chapters.
For now, I want to be 100% certain on a very important story element before I write any chapters. Although that story element won't be mentioned until late in the series, it's important to have correct from the first episode. So that's why I'm not posting it just yet.